THE GOLDEN RATIO
Divide any Fibonacci number by the one before it and you get an approximation of the golden ratio, 1.6180339887498948420…, a number that continues on forever with no discernible pattern. (This is called an ‘irrational number’.) The quotient oscillates above and below this number as you progress along the series, and the larger the pair of Fibonacci numbers, the closer the approximation.
So, for example, 55 divided by
34 is 1.617647…, an accurate representation of the golden ratio to two or three decimal places.